With the release of Final Cut Pro 10.1, Apple changed the way projects and media are managed by introducing the "Library".
Watch this video by Larry Jordan:
Still using 10.0.9 or earlier? Here's how to share a project:
Plug in the external hard drive & launch Final Cut Pro X.
Navigate to the Project Library and right-click on the project you'd like to share. Then select "Duplicate Project..." or press Command-D:
Select the correct location of the external drive from the drop down menu and make sure to choose "Duplicate Project and Referenced Events". Select OK.
Handy tip: To save space and reduce the size of the folders being copied, uncheck "Include Render Files".
Thats it, you're done! When Final Cut Pro X is launched on another machine with that drive connected, your project will be ready to go in the Project Library.